Home heating oil is basically the very same as diesel (#2 fuel oil) - there is no advantage with using home heating oil , except the possibility of enriching one's attorney, since it's illegal (no road fuel tax, and likely not a legal formulation with respect to sulfur).
Anyway, the "octane rating" is based on the performance of a motor fuels as compared to isooctane (100) versus normal heptane (0), and it's a measure of how quickly the fuel-air mixture will combust.
Cetane rating is essentially the time-delay from injection to ignition of the fuel-air mixture. Cetane-improver is unnecessary for a diesel designed to run on 40 cetane.
Adding motor oil to diesel fuel is unwise, since all the components don't burn; ashless 2-cycle oil is OK, but I use FPPF or CRC additives rather than 2-cycle oil.
Adding gasoline is also not just unwise but dangerous. The diesel-gaso mixture will now have the flash/fire point of gaso - and damage to the engine is quite possible (ever notice the prohibition against using ether to start a glow-plug equipped engine?). The gaso will also defeat the addition of lubricating additves to the diesel.
'94 Barth 28' Breakaway M/H ("StaRV II") diesel pusher: Spartan chassis, aluminum birdcage construction. Peninsular/AMG 6.5L TD (230HP), 18:1, Phazer, non-wastgated turbo, hi-pop injectors, 4L80E (Sun Coast TC & rebuild, M-H Pan), Dana 80 (M-H Cover), Fluidampr, EGT, trans temp, boost gage. Honda EV-4010 gaso genset, furnace, roof air, stove, microwave/convection, 2-dr. 3-way reefer. KVH R5SL Satellite. Cruises 2, sleeps 4, carries 6, and parties 8 (parties 12 - tested).
Stand-ins are an '02 Cadillac Escalade AWD 6.0L and an '06 Toyota Sienna Limited.